Strongly interacting two photon random walk in an array of single atom beamsplitters

Few photon quantum walk is a powerful tool for quantum simulation. However, most theoretical and experimental works related to this topic have been focused on linear beam splitter arrays, which lack photon-photon interactions. Here we propose a novel way of implementing a strongly interacting two photon discrete time quantum walk. We use single atom beam splitters to induce strong photon-photon interaction. Photonic quantum walks in such a nonlinear beam splitter array are still poorly understood. In this work, we theoretically investigated the two photon correlation functions at the output and observed strong photon-photon interaction which yield various types of photon statistics. Finally, we propose a practical realization of our random walk based on time-multiplexed synthetic dimensions. Our proposal has opened the door for a novel approach of quantum simulation using photons.